A Bimodality Test in High Dimensions

We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying the correct clusters more difficult. In addition to the original conservative test, we propose a practical test with the same asymptotic behavior that performs well for a moderate number of points and moderate dimensionality. ACM Computing Classification System (1998): I.5.3.

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.